Detecting orbital debris

ABSTRACT

A network device determines an exposure time associated with an image sensor coupled to a spacecraft for capturing an image of a target object orbiting the Earth. The network device computes a maximum relative angular velocity associated with the target object based on the exposure time and a dimension of a pixel of the image sensor. The network device identifies a first pointing direction of the image sensor for initiating a search for the target object. The network device generates a first angular velocity probability distribution map for the target object and divides the first angular velocity probability distribution map into a first set of angular velocity regions (AVRs). The network device selects a first AVR from the first set of AVRs for scanning by the image sensor and generates a search schedule that includes a first entry for informing the spacecraft to scan the first AVR.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.13/647,943, entitled “Detecting Orbital Debris”, filed on Oct. 9, 2012,which claims the benefit of U.S. Provisional Application Ser. No.61/544,252, entitled “Searching for Orbital Debris with MultipleSatellites using Angular Velocity Regions”, filed on Oct. 6, 2011, andU.S. Provisional Application Ser. No. 61/553,819, entitled “Detection ofOrbital Matter”, filed on Oct. 31, 2011, the entirety of which arehereby incorporated by reference as if fully set forth therein.

TECHNICAL FIELD

This document generally relates to detecting orbital debris.

BACKGROUND

Typically, man-made objects sent into space have limited usefullifetimes. Some of these objects remain in orbit about the Earth evenwhen they no longer serve any useful purpose.

SUMMARY

The present disclosure describes systems and techniques by which orbitaldebris may be detected by an image sensor on board a spacecraft. Theimage sensor detects orbital debris using a search schedule, which isbased on partitioning the space of angular velocities of the orbitaldebris into angular velocity regions (AVRs) and detecting orbital debrisby scanning selected AVRs. The image sensor is slewed at an angularspeed and in a direction corresponding to the central angular velocityassociated with the AVR presently searched. The angular speed anddirection of slew of the image sensor changes as the AVR searched ischanged.

In one aspect, a network device determines an exposure time associatedwith an image sensor coupled to a spacecraft for capturing an image of atarget object orbiting the Earth. The image sensor includes a matrix ofphoto-sensitive pixels. The network device computes a maximum relativeangular velocity associated with the target object based on the exposuretime and a dimension of a pixel in the matrix of pixels. The networkdevice identifies a first pointing direction of the image sensor forinitiating a search for the target object. The network device accessestarget object orbital data. The network device generates, based on thefirst pointing direction and the target object orbital data, a firstangular velocity probability distribution map that indicatesprobabilities of the target object having different angular velocitiesas viewed by the image sensor when the image sensor is pointing in thefirst pointing direction. The network device divides the first angularvelocity probability distribution map into a first set of angularvelocity regions (AVRs), each AVR having a central angular velocity andhaving a size corresponding to the computed maximum relative angularvelocity. The network device selects a first AVR from the first set ofAVRs for scanning by the image sensor. The network device generates asearch schedule that includes a first entry for informing the spacecraftto scan the first AVR. Scanning the first AVR comprises positioning theimage sensor at the first pointing direction and rotating the imagesensor at an angular speed and direction corresponding to the centralangular velocity of the first AVR.

Implementations may include one or more of the following features.Computing the maximum relative angular velocity may comprise dividingthe pixel dimension by the exposure time. The network device maydetermine, for the first entry added to the search schedule, whether anadditional scan of the first AVR is to be performed. Responsive todetermining that an additional scan of the first AVR is to be performed,the network device may update the search schedule with a second entryfor informing the spacecraft to scan the first AVR.

The network device may determine whether the search schedule iscomplete. Based on determining that the search schedule is not complete,the network device may identify a second pointing direction of the imagesensor at the end of scanning the first AVR. The network device maygenerate, based on the second pointing direction and the target objectorbital data, a second angular velocity probability distribution mapthat indicates probabilities of the target object having differentangular velocities as viewed by the image sensor when the image sensoris pointing in the second pointing direction. The network device maydivide the second angular velocity probability distribution map into asecond set of AVRs. The network device may select a second AVR from thesecond set of AVRs for scanning by the image sensor. The network devicemay update the search schedule for the image sensor with a second entryfor informing the spacecraft to scan the second AVR. Scanning the secondAVR may comprise positioning the image sensor at the second pointingdirection and rotating the image sensor at an angular speed anddirection corresponding to the central angular velocity of the secondAVR.

The size of the second set of AVRs may be smaller than a size of thefirst set of AVRs. The network device may identify a third pointingdirection of the image sensor at the end of scanning the second AVR. Thenetwork device may generate, based on the third pointing direction andthe target object orbital data, a third angular velocity probabilitydistribution map that indicates probabilities of the target objecthaving different angular velocities as viewed by the image sensor whenthe image sensor is pointing in the third pointing direction. Thenetwork device may divide the third angular velocity probabilitydistribution map into a third set of AVRs, the size of the third set ofAVRs being smaller than the size of the second set of AVRs.

The network device may determine whether the search schedule iscomplete. Based on determining that the search schedule is complete, thenetwork device may transmit the search schedule to the spacecraft.

The spacecraft may receive the search schedule from the network device.The spacecraft may read the first entry in the search schedule. Based onreading the first entry, the spacecraft may slew the image sensorstarting from the first pointing direction for scanning the first AVR.The spacecraft may enable the image sensor for recording sensor readingsas the image sensor scans the first AVR.

The spacecraft may determine whether there are additional entries in thesearch schedule. Based on determining that there are additional entriesin the search schedule, the spacecraft may read the next entry in thesearch schedule. The next entry may include information for thespacecraft to scan a next AVR. Scanning the next AVR may comprisepositioning the image sensor at the next pointing direction and rotatingthe image sensor at an angular speed and direction corresponding to thecentral angular velocity of the next AVR. Responsive to reading the nextentry, the spacecraft may slew the image sensor starting from the nextpointing direction for scanning the next AVR. The spacecraft may enablethe image sensor for recording sensor readings as the image sensor scansthe next AVR.

The target object may include orbital debris. The exposure time mayinclude a time used by the image sensor for recording sensor readings.The exposure time may be based on at least one of a noise floor andthreshold signal-to-noise ratio (threshold SNR) associated with theimage sensor.

The exposure time may be based on at least one of size and distance ofthe target object. The size of each AVR may be at most as large as themaximum relative angular velocity.

The first set of AVRs may include AVRs of varying sizes, the size of anAVR based on a magnitude of an angular velocity of the target object atthe center of the AVR. The size of an AVR may be proportional to themagnitude of the angular velocity at the center of the AVR, the sizebeing smaller for a smaller angular velocity at the center of the AVR incomparison to a larger angular velocity at the center of the AVR.

The first set of AVRs may include AVRs with a shape that is one of acircular shape and a hexagonal shape. Selecting a first AVR from thefirst set of AVRs may comprise selecting the first AVR based on one of arandom selection strategy and a probability of detection of the targetobject that is associated with each AVR in the first set of AVRs. Thenetwork device may include a ground-based computing device.

Implementations of the above techniques include a method, a computerprogram product and a system. The computer program product is suitablyembodied in a non-transitory machine-readable medium and includesinstructions executable by one or more processors. The instructions areconfigured to cause the one or more processors to perform the abovedescribed actions.

The system includes one or more processors and instructions embedded ina non-transitory machine-readable medium that are executable by the oneor more processors. The instructions, when executed, are configured tocause the one or more processors to perform the above described actions.

The details of one or more aspects of the subject matter described inthis specification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an example of a system that may be used for detectingorbital debris.

FIG. 2A illustrates an exemplary reasonable angular velocitydistribution (RAVD) plot of orbital debris relative to an image sensorfor a given image sensor pointing direction.

FIG. 2B illustrates a portion of an exemplary image sensor showing thearea covered by four pixels of the image sensor.

FIGS. 3A and 3B illustrate examples of AVR maps.

FIG. 4 illustrates an exemplary process that may be used for developingan AVR-based search schedule for an image sensor for detecting orbitaldebris.

FIG. 5 illustrates an exemplary process that may be used for searchingfor orbital debris using an image sensor on board a satellite.

FIG. 6 illustrates an exemplary search performed by an image sensor onboard a satellite for detecting orbital debris.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

Some man-made objects that are sent into space may remain in orbit aboutthe Earth after their useful functional lifetimes, or after they haveceased to be operational, or both. Such space objects are a type oforbital debris. The amount of man-made debris in orbit is increasing ata rapid pace as more and more spacecraft are launched into orbit by bothgovernments and, more recently, private companies. Examples of man-madeorbital debris include derelict spacecraft and upper stages of launchvehicles, carriers for multiple payloads, debris intentionally releasedduring spacecraft separation from its launch vehicle or during missionoperations, debris created as a result of spacecraft or upper stageexplosions or collisions, solid rocket motor effluents, and tiny flecksof paint released by thermal stress or small particle impacts. Inaddition to man-made objects in orbit, orbital debris also includesobjects that consist of natural components, such as, for example, rockand ice.

Most orbital debris reside within 2,000 km of the Earth's surface, withsome large concentrations of debris found at an altitude of 750-800 kmfrom the Earth's surface. Some of the debris, such as debris in orbitsbelow 600 km, normally fall back to Earth within several years. However,at higher altitudes, the orbital debris will typically remain in Earthorbit for longer periods. For example, at altitudes of 800 km, the timefor orbital decay is often measured in decades. Above 1,000 km, orbitaldebris will normally continue circling the Earth for a century or more.

Orbital debris may pose a risk to continued reliable use of space-basedservices and operations, and to the safety of persons and property inspace and on Earth. For example, operational spacecraft may collide witha large space object, such as a derelict satellite, which can causesignificant damage to the operational spacecraft. Most orbital debristhat re-enters the Earth's atmosphere is destroyed due to the severeheating that occurs during reentry, and debris that survives reentry ismost likely to fall into the oceans or other bodies of water or ontosparsely populated regions. Nevertheless, a possibility exists that someof the debris may fall in inhabited areas, which may result in seriousinjury to humans or animals or significant property damage.

It may be useful to detect orbital debris in space and examine theirtrajectories to identify possible close encounters with operationalspacecraft, or with terrestrial objects. For example, surveillancenetworks may monitor the trajectories of orbital debris, such that ifdebris is projected to come within a few kilometers of an operationalspacecraft, the latter may be maneuvered away from the debris if thechance of a collision exceeds a certain threshold probability.

Orbital debris, which is also referred to as Resident Space Objects(RSOs) or space objects, may be detected using a Low Earth Orbit (LEO)satellite network. One or more cameras or telescopes, which includeimage sensors, mounted on a satellite may be used to capture images oforbital debris. The image sensor in a telescope or camera may be, forexample, a charge-coupled device (CCD) image sensor having a matrix ofphoto-sensitive pixels that convert incoming photons into electricalsignals to form an image.

In order to detect dim orbital debris, the exposure time of an imagesensor is typically increased. The exposure time, which is also referredto as the integration time, is the amount of time that the image sensorallows photon energy to accumulate for a given image that is generated.To enable detection of an object, the exposure time is typicallyselected such that the amount of energy accumulated from photonsreceived from the object results in an electrical signal having astrength greater than the noise floor of the sensor, with the likelihoodof detection increasing as the amount of energy and, thus, the strengthof the generated signal increases above the noise floor. For example, ina CCD image sensor, the integration or exposure time is the amount oftime that electrical charges generated by photons are allowed toaccumulate on, for example, a semiconductor-oxide interface in eachpixel of the sensor when an image is generated. Less photons arereceived from a dim object than from a bright object, and, therefore,exposure time is typically increased to enable detection of dim objects.

Increasing the exposure time of the image sensor to better detect dimobjects works well when the detected space object is stationary relativeto the camera, but may not work as well when the object is movingrelatively quickly. For example, if the space object is moving, then theenergy received from the space object may be smeared across the pixelsof the image sensor, preventing any given pixel from receivingsufficient energy to enable detection. Although it is sometimes possibleto produce an image by, for example, adding the signals of each pixelthat received energy from the dim object, such additive techniques canbe very difficult to apply when detecting very dim space objects due tonoise problems. Therefore, it may be useful to implement techniques bywhich image sensors mounted on one or more satellites can detect orbitaldebris that may be moving relative to the satellites.

In one implementation, the probability of detecting orbital debris by animage sensor mounted on a satellite may be improved by moving the imagesensor at the same or approximately the same angular velocity as thespace object. In this way, the space object generally stays at the sameplace relative to the image sensor, and, thereby, allows each pixel ofthe image sensor to generate a much stronger electrical signal. Withvery dim space objects, this technique can greatly increase theprobability of detection. In this context, angular velocity refers to apseudo-vector that has a magnitude corresponding to the angular speed(that is, rotational speed) and a direction that specifies both thedirection of rotation and the axis of rotation.

The above technique uses knowledge of the trajectories of space objects.Although orbital debris can be very dim, the debris typically moves withpredictable and bounded trajectories, particularly if the debris hasstable (that is, non-escape velocity) orbits. In addition, the angularvelocities of the orbiting debris tend to “cluster” into similar areas,with most orbits being roughly perpendicular (in angular velocity) tothe detector's orbit. Therefore, the space of possible angularvelocities of the orbital debris can be partitioned into “cells” ofsimilar angular velocities, which are referred to as Angular VelocityRegions (AVRs). Orbital debris in each AVR can be detected by slewingthe image sensor at the same angular speed and in the same direction asthe angular velocity corresponding to the center of the AVR.

Methods, systems and devices are described in the following sections fordeveloping and implementing a search schedule for detecting orbitaldebris. The search schedule is based on partitioning the space ofpossible angular velocities into AVRs and detecting orbital debris byscanning selected AVRs using an image sensor mounted on a satellite. Forthe purposes of this discussion, the terms orbital debris, debris, RSOand space object are used synonymously. The terms camera, image sensor,optical sensor and sensor are used interchangeably to refer to the sameitem, that is, an image sensor capable of detecting orbital debris. Inaddition, though the remaining sections are described in reference to animage sensor mounted on a satellite, the techniques described here areequally applicable to multiple image sensors mounted on one or moresatellites, or other spacecraft.

FIG. 1 illustrates an example of a system 100 that may be used fordetecting orbital debris. The system 100 includes a satellite 105 withan image sensor 110 mounted on board the satellite. The satellite 105communicates with satellite gateways 115 a and 115 b over satellitelinks 130 a and 130 b respectively. Satellite gateways 115 a and 115 bare connected to a network operations center (NOC) 120 on the Earth'ssurface through the terrestrial network 125. Debris, such as 140 and145, are moving in orbits around the Earth.

The satellite 105 is a satellite orbiting the Earth that is capable ofcapturing images of orbiting debris. For example, the satellite 105 maybe a satellite in a network of LEO satellites at an altitude between 160kilometers and 2000 kilometers. The satellite 105 also may be a MediumEarth Orbit (MEO) satellite that is orbiting the Earth at an altitude inthe range of 2000 kilometers to 24000 kilometers, or a Geostationary(GEO) satellite that is at an orbit approximately 36000 kilometers abovethe Earth's equator. The satellite 105 also may represent a spacecraftother than a satellite that is capable of capturing images. For example,the satellite 105 may be the International Space Station (ISS).

The satellite 105 includes one or more image sensors that are coupled tothe satellite, which may be used for detecting orbiting debris, such as140 or 145. One such image sensor 110 is shown in FIG. 1. The imagesensor 110 is configured for capturing images, including images oforbiting objects such as orbiting debris 140 or 145. The image sensor110 may be a CCD image sensor or an active-pixel sensor (APS) such as acomplementary metal-oxide-semiconductor (CMOS) APS. The image sensor 110may be an optical sensor that is capable of capturing optical energy ona visible wavelength. Alternatively, the image sensor 110 may be aninfrared detector that can detect electromagnetic radiation on infraredwavelengths that may be generated by space objects. In someimplementations, the image sensor 110 also may be capable of detectingelectromagnetic energy on other wavelengths, such as gamma ray, x-ray,ultraviolet, microwave or radio waves.

The image sensor 110 is mounted on a gimbal device that is coupled tothe satellite 105. The gimbal device is a pivoted support device thatallows the image sensor 110 to be rotated about one or more axes. Insome implementations, the gimbal device may include a set of threegimbals, with one mounted on the other with orthogonal pivot axes. Theimage sensor 110 may be mounted on the innermost gimbal such that theimage sensor 110 remains independent of the movement of the gimbaldevice itself due to the orbiting movement of the satellite. Therefore,the image sensor 110 may be kept upright with respect to a referenceframe despite the satellite's pitching and rolling.

The satellite 105 includes one or more processors and storage media,such as a hard drive or flash memory, which store instructions that canbe executed by the processors. By executing the instructions, thesatellite 105 can operate the gimbal device to slew the image sensor 110at a constant angular velocity. In this context, to slew the imagesensor 110 means to rotate the image sensor 110 about a fixed axis in aspecified direction at a specified rate. In some implementations, theimage sensor 110 may be slewed in more than one direction sequentially.

Typically, the image sensor 110 is oriented to point outwards in spaceso that it may detect space objects through, for example, an aperture inthe satellite 105. In some implementations, the orientation of the imagesensor 110 is expressed with respect a reference frame that is fixed inthe body frame of the sensor's patent object, that is, the satellite105. For example, the orientation of the image sensor 110 relative tothe satellite 105's reference frame, which also may be referred to asthe sub-component reference frame, may be expressed by an azimuth and anelevation. The azimuth may be an angle measured from the X-axis in theXY-plane of the sub-component reference frame about its Z-axis in thecounter-clockwise direction. The elevation may be expressed as the anglebetween the XY-plane of the sub-component reference frame and the imagesensor pointing measured toward the positive Z-axis. Alternatively, theorientation of the image sensor 110 may be expressed by yaw, pitch androll angles measured from respective axes of the satellite 105'sreference frame.

In some implementations, the origin of satellite 105's reference framemay be the center of the satellite 105. The satellite 105 itself mayhave an orientation with respect to the Earth or other celestial bodies,lines of force of magnetic and gravitational fields, or other givendirections in space. For example, the satellite 105's orientation withrespect to the Earth may be specified by a nadir vector and a velocityvector. The nadir vector is a vector extending from the center of thesatellite 105 to the center of the Earth, and the velocity vector is avector extending from the center of the satellite 105 to a point in thedirection in which the satellite is traveling in orbit. In otherimplementations, the orientation of the satellite 105 may be specifiedusing some other suitable reference, such as a neighboring spacecraft orstarfield databases. In some implementations, the orientation of thesatellite 105 and that of the image sensor 110 may be considered to bethe same.

The image sensor 110 may capture images of space objects that appear inits field of view (FOV) in the direction in which the image sensor 110is oriented. The FOV may be thought of as a pyramid with a vertex thatis at the focal point of the image sensor 110 and an axis extending inthe direction the image sensor 110 is currently pointing. Typically, theFOV of the image sensor 110 is much smaller than the area of interest,which is the region of space in which orbiting debris are to bedetected. For example, the area of interest may be several thousandkilometers in front of (or behind) the image sensor 110. However, theFOV may cover an area with an arc of 90 degrees in both the X-axis andthe Y-axis with respect to the nominal (that is, un-gimbaled) directionof the image sensor 110 in the reference frame of the satellite 105.

The one or more processors on board the satellite 105 may executeinstructions that cause the gimbal device to slew the image sensor 110such that the image sensor scans the entire area of interest, that is,the FOV of the image sensor 110 covers the desired region of space.Techniques for determining areas of interest and rotating the imagesensor 110 for scanning an area of interest are described in thefollowing sections.

The satellite gateways 115 a and 115 b are terrestrial antennas thattransmit and receive data in the form of electromagnetic radiation, suchthat communication with the satellite 105 are facilitated. The satellitegateways are controlled by the NOC 120. The NOC 120 is a centrallocation from which network monitoring and control is exercised over thesatellite 105. The NOC 120 may include one or more physical locations onthe Earth's surface and may be managed by any suitable entity, such asbusiness organizations, public utilities, universities, and governmentagencies, for overseeing operation of the satellite network thatincludes the satellite 105.

The NOC 120 communicates with the satellite gateways 115 a and 115 b viathe network 125, which may include a circuit-switched data network, apacket-switched data network, or any other network able to carry data,such as Internet Protocol (IP)-based or asynchronous transfer mode(ATM)-based networks, including wired or wireless networks. For example,the network 125 may a Local Area Network (LAN) or a Wide Area Network(WAN). The network 125 may include the Internet, analog or digital wiredand wireless networks (such as IEEE 802.11 networks, Public SwitchedTelephone Network (PSTN), Integrated Services Digital Network (ISDN),and Digital Subscriber Line (xDSL)), Third Generation (3G) or FourthGeneration (4G) mobile telecommunications networks, a wired Ethernetnetwork, a private network such as an intranet and/or any other deliveryor tunneling mechanism for carrying data, or any appropriate combinationof such networks. In addition, the network 125 may be configured tohandle secure traffic such as secure hypertext transfer protocol traffic(HTTPS) or virtual private networks (VPN) such that the connectionsbetween the NOC 120 and the satellite gateways 115 a and 115 b may besecure connections, such as using VPN or HTTPS. However, in otherimplementations, the connections may be unsecured connections.

In some implementations, the NOC 120 and one or both satellite gateways115 a and 115 b are co-located. For the purposes of this discussion, theNOC 120 and the satellite gateways 115 a and 115 b are collectivelyreferred to as the ground-based system (GBS).

The NOC 120 includes one or more computing devices configured to executeinstructions stored on storage media, such as hard drives and flashmemory. In some implementations, search schedules are determined throughthe execution of the instructions by the computing devices in the NOC120. A search schedule includes information for rotating the imagesensor 110 for searching a specific area of interest for detectingorbital debris. Different search schedules may be determined fordifferent regions of interest based on AVRs. For example, the orbitaldebris 140 and 145 may correspond to different search spaces, such thatthe search schedules that detect them may be different. Thedetermination of search schedules is described in detail in thefollowing sections.

The NOC 120 transmits one or more search schedules to the satellite 105through the gateways 110 a and/or 110 b, which communicate with thesatellite through satellite channels 130 a and 130 b respectively. Thesatellite channels 130 a and 130 b are wireless communication channels.Each satellite channel includes an uplink communication path for thecorresponding gateway to send to the satellite 105 control and telemetryinformation, which includes the search schedules for the image sensor110. Each satellite channel may also include a downlink communicationpath for the satellite 105 to send data to the gateways 115 a and/or 115b. The data may include image data captured by the image sensor 110based on the search schedules. The gateways send the data received fromthe satellite 105 to the NOC 120. Subsequently the NOC processes theimage data to determine whether orbital debris can be detected from theimage data, and if detected, the direction and trajectory for thedebris.

As indicated previously, an area of interest is compartmentalized intoAVRs that are fed as input for generating search schedules for the imagesensor 110. A search schedule may correspond to a set of AVRs that arescanned in a predetermined order to search efficiently the area ofinterest. The determination of AVRs uses knowledge of the angularvelocities of orbital debris. In some implementations, the space ofangular velocities of orbital debris is initially decomposed intosub-spaces of similar angular velocities. This may be performed by thecomputing devices at the NOC 120. In other implementations, theprocessors on board the satellite 105 may be configured to perform thedecomposition.

In some implementations, the NOC 120 or the satellite 105 maypre-compute a variety of reasonable angular velocity distribution (RAVD)plots for a multitude of different image sensor 110 pointing directions(that is, orientations). Each RAVD plot is a plot of a distribution thatshows the probability of orbital debris having a particular angularvelocity relative to the image sensor 110 when the image sensor ispointing in a particular pointing direction. The RAVD plot allowsidentification of the subset of angular velocities that have a higherprobability to correspond to the angular velocities of orbiting debris,given the image sensor's pointing direction.

Typically, the RAVD plot is computed by accessing known debris orbitdata corresponding to debris that the satellite 105 is attempting todetect. Known debris orbit data is information that has been catalogued(for example, by the U.S. Government) that describes the orbits aroundthe Earth of different types of known, non-escape velocity debris.Selection of the proper known debris orbit data typically requiresknowledge of the type of debris of interest (for example, debris above 1cm in size) and the target distance, that is, the distance from thefocal point of the image sensor 110 to the debris of interest (forexample, 3000 km from focal point of image sensor). Once selected, theknown debris orbit data may be processed based on the known pointingdirection (orientation) of the image sensor 110 to generate aprobability distribution of reasonable angular velocities that may beused to estimate which angular velocities are more likely to correspondto the angular velocities of orbiting debris of interest.

In some implementations, the RAVD plot may be generated by using anapriori probability distribution for debris orbits, which is given byp(x), where x is a random variable corresponding to the debris orbit.Using standard probabilistic computation and the known behavior of theimage sensor 110, an observation probability p(y|x) may becharacterized, where p(y|x) is the probability that the observation ycorresponds with a known orbit x. That is, p(y|x) indicates theprobability that the image sensor 110 would give a reading y when adebris is known to be present in orbit x. Using standard estimation anddetection techniques, such as Bayes Rule, p(x|y) may be obtained fromp(y|x), where p(x|y) is the probability that there is debris in orbit xwhen the image sensor provides a reading y. The distribution p(x|y) maybe sampled using standard techniques to generate the RAVD plot.

FIG. 2A illustrates an exemplary reasonable angular velocitydistribution (RAVD) plot 200A of orbital debris relative to an imagesensor for a given image sensor pointing direction. The plot 200A may becomputed, for example, by the NOC 120. The plot 200A includes a graph210 and a key 212 for identifying the percentage distributions indicatedon the graph 210.

The plot 200A provides a normalized probability distribution ofreasonable angular velocities at different orbits in which debris arelikely to be detected, at a certain target distance from an image sensorhaving a particular orientation or pointing direction on board asatellite. In some implementations, the plot 200A may be customized fora specific image sensor, for example, the image sensor 110. As statedabove, the plot 200A may be generated by processing known debris orbitdata based on the pointing direction of the image sensor.

The graph 210 displays the probability distribution of reasonableangular velocities at the given target distance, with each point in theplot indicating a normalized probability of orbital debris having thecorresponding angular velocity. In this exemplary RAVD plot, thedimension of the angular velocities is expressed in micro-radians persecond (μRads/sec), with the X- and Y-axes of the graph 210 indicatingvalues of the X- and Y-components of the angular velocities.

The points in the graph 210 are coded using a suitable representation,for example, color coded, with different codes representing differentnormalized probabilities of orbital debris having the correspondingangular velocities. The values provided by the key 212 are percentilescomputed as a percentage of a maximum probability constant. Therefore,an area on the graph 210 that corresponds to a percentile value of80%-100% indicates a set of angular velocities that are more likely tocorrespond to angular velocities of orbiting debris than the set ofangular velocities indicated by areas on the graph 210 corresponding tolower percentile values, such as, for example, 20%-40%.

To estimate the actual probability of orbital debris having an angularvelocity within a particular set of angular velocities, the probabilityfunction used to generate the graph 210 is first multiplied by themaximum probability constant to, thereby, remove the normalization.After removing the normalization, the probability of orbital debrishaving an angular velocity within a particular set of angular velocitiescorresponding to a 2D area or region of the graph 210 may be calculatedby integrating in two dimensions the non-normalized probability functionover the particular set of angular velocities (that is, determining thevolume under the 2D curve). The result of the integration is theprobability that orbital debris have an angular velocity within theregion of angular velocities of interest. For example, to determine theprobability that orbital debris will have an angular velocity within theregion of angular velocities corresponding to the 80%-100% triangle onthe right-side of the graph 210, the probability function used togenerate the graph 210 would have to be multiplied by the maximumprobability constant and then would have to be integrated over the X andY components of angular velocities to determine the volume under the80%-100% triangle.

In some implementations, the plot 200A is used in implementing a searchschedule that is used to scan for orbiting debris by focusing the scanon sets of angular velocities that plot 200A indicates have a higherprobability of corresponding to the angular velocities of orbitingdebris. Adopting such a search schedule may lead to an increase in boththe accuracy and the efficiency of orbital debris detection.

In some implementations, an AVR map is developed based on the plot 200.An AVR is a grouping or “region” of angular velocities that aresufficiently close to one another such that if an image sensor wereslewed at an angular velocity corresponding to the center of the AVR,the image sensor would detect debris moving at any angular velocitywithin the AVR as if that debris were completely stationary relative tothe image sensor. The concept of an AVR may be best illustrated byconsidering the pixels of an image sensor and recognizing that a movingobject is deemed stationary relative to the image sensor if it does notmove from an area covered by one pixel to an area covered by a secondpixel during the exposure time of the image sensor. It is axiomatic thatorbiting debris that move at the exact same angular velocity as theimage sensor are stationary relative to the image sensor (assuming wedisregard radial movement). Orbiting debris that move at a differentangular velocity than the image sensor will, of course, move relative tothe image sensor and its pixels.

For example, FIG. 2B illustrates a portion of an exemplary image sensor200B showing the area covered by four pixels of the image sensor. Thefour pixels are represented by 222, 224, 226 and 228. The initialposition of an orbital debris at the start of the exposure time of theimage sensor 200B is indicated by 232. The position of the orbitaldebris at the end of the exposure time of the image sensor 200B isindicated by 234. The arrow 236 indicates the movement of the orbitaldebris from the position 232 to the position 234 during the time theimage sensor 200B captured images of the orbital debris. As shown inFIG. 2B, the angular velocity of the orbital debris is such that thedebris remains within the area covered by a single pixel, that is, pixel224, during the exposure time of the image sensor 200B.

Therefore, FIG. 2B indicates that if the relative movement between thedebris and the image sensor is small enough such that the object failsto move from the area covered by one pixel of the image sensor to anarea covered by a different pixel during the exposure time, the objectwill, despite its movement, be detected by the image sensor as if itwere completely stationary.

An AVR, therefore, is tied to the pixel dimension of the image sensorand encompasses all angular velocities from a particular center angularvelocity that would be deemed stationary by an image sensor when theimage sensor is slewed at an angular speed and in a directioncorresponding to the center angular velocity. Assuming that the pixelsare square, the resulting Angular Velocity Regions (AVRs) may beapproximately circular.

The orbital angular velocities indicated by the plot 200A may besearched for debris detection by slewing an image sensor at ratessimilar to the angular velocities being scanned. This may be performedefficiently by partitioning the space of reasonable angular velocitiesdepicted in the plot 200A into an AVR map and then scanning the AVRs oneat a time to detect debris. An AVR may be searched or scanned by movingthe image sensor at an angular speed and in a direction that correspondsto the angular velocity at the center of the AVR. Any debris having anangular velocity within the AVR will appear stationary to the imagesensor. Because the debris appears stationary to the image sensor, theimage sensor is able to maximize the amount of energy received from thedebris, making detection of dim debris more likely. Moreover, bydecomposing the space of reasonable angular velocities in this manner,it may be possible to focus the searching effort on AVRs that are morelikely to have debris, and thus detect debris faster and moreefficiently.

An AVR map for the purposes described above may be constructed byoverlaying a set of AVRs on to the plot 200. The set of AVRs may beconstructed as described in the following sections.

Each set of AVRs may be customized for a specific image sensor. The sizeof an AVR and/or the number of AVRs depend on the characteristics of theimage sensor and properties of the orbital debris to be detected. Forexample, the size of an AVR may depend on the noise floor and thresholdsignal-to-noise ratio (SNR) of the image sensor. The noise floor is ameasure of the noise signal created at the image sensor from the sum ofall the noise sources and unwanted signals in the system that affect theimage sensor. The noise floor is a function of the thermal noise in theimage sensor, the temperature of extra-terrestrial space in which thesatellite is moving, and dark currents that may be generated in theextra-terrestrial space, among other factors. The noise floor affectsthe measurements made by the image sensor. For example, the exposuretime may be less for an image sensor that has a lower noise floorcompared to an image sensor that has a higher noise floor.

The noise floor contributes to the threshold SNR of the image sensor,which provides a measure of the amount of detection energy that theimage sensor has to capture such that an accurate detection may be madeof orbital debris. Therefore, the threshold SNR is associated with theprobability of detection accuracy and indicates a degree of sensitivityof the image sensor.

Information on the noise floor, threshold SNR and other suitablephysical parameters of the image sensor may be obtained prior to usingthe image sensor for searching orbital debris. For example, theparameters may be provided in a datasheet from the manufacturer.Alternatively or additionally, the parameters may be obtained bycalibration of the image sensor during test runs and downloaded from thesatellite to the NOC.

The physical characteristics of the orbital debris, such as brightness,also may be obtained prior to using the image sensor. In someimplementations, the debris brightness manifests itself at the imagesensor as the number of photons per second that are captured by theimage sensor. A debris that is brighter results in a greater number ofphotons per second captured, compared to a debris that is less bright.

The brightness of the debris affects the exposure time of the imagesensor. For brighter debris, more energy may be captured relativelyquickly and therefore the exposure time may be less, compared to theamount of exposure time that may be needed for capturing an equivalentamount of energy from a less bright debris. Therefore, the exposure timeof the image sensor can be inversely proportional to the debrisbrightness.

The debris brightness depends on the size of the debris and the targetdistance at which the debris is detected. Debris of a larger size may bebrighter than debris of smaller size; consequently, larger debris may bedetected with less exposure time compared to smaller debris. The size ofthe debris as seen from the image sensor varies inversely with thetarget distance. The debris at a greater target distance may appearsmaller to the image sensor compared to debris at a closer targetdistance, which may result in the debris at the greater target distanceappearing less bright to the image sensor compared to debris at thecloser target distance. Therefore, the image sensor may be configuredwith a longer exposure time when searching for debris at a greatertarget distance, while in comparison the exposure time may be shorterwhen searching for debris at a closer target distance.

In addition to the parameters discussed above, the size of an AVR maydepend on the dimension of the pixels of the image sensor. A pixel isthe smallest scalar element of a multi-component representation of theimage sensor and indicates the smallest addressable unit of the imagesensor. In some implementations, all pixels of the image sensor have thesame dimension, which is based on the FOV of the image sensor and thenumber of pixels that make up the image sensor, and may be expressed asFOV/number of pixels. Each pixel may have a square shape and the widthof a pixel may be expressed as an angle. For example, for an imagesensor with a 10 radians FOV and 10⁶ pixels, the width of each pixel maybe 10⁻⁵ radians. Therefore, a pixel may capture images in a squarepyramidal area that has a diameter of 10⁻⁵ radians at the surface of theimage sensor, with the vertex of the pyramid being at the focal point ofthe image sensor.

Once all the parameters above are determined, the maximum relativeangular velocity A may be computed. A indicates the maximum orbitalangular velocity, relative to the angular velocity at which thesatellite is moving, at which debris may be detected as if they werestationary by the image sensor. A is calculated based on the variousparameters noted above, such as the noise floor of the image sensor, thebrightness, size and target distance of the debris, and the pixeldimension. A may be computed as a function of the pixel dimension andthe exposure time. For example, the maximum relative angular velocity Amay be expressed as (pixel dimension/exposure time).

In some implementations, A may be computed based on the following. Let Edenote the energy needed to trigger a positive reading (in Joules) onthe image sensor, while E′ denotes the power received at the sensor fromthe orbital debris (in Watts). The exposure time t that may be used toachieve a reading is given by the equation t=E/E′. E′ is typicallyestimated based on the reflectivity of the debris, the angle of the sun,the aperture of the image sensor, and many other parameters. Let θ be afixed angle covered by the pixel pitch. Then the maximum angularvelocity A may be given by the equation A=θ/t.

The above example of an equation for computing A does not considerpartial detections or detections with probability. At low light levels,the image sensor may be affected by noise to a large extent, which mayincrease the exposure time.

After determining A, the AVRs may be computed by dividing the space ofreasonable angular velocities into a set of AVRs. For example, the plot200A may be divided into a set of AVRs. In some other implementations,the space of all possible angular velocities (that is, the whole plot200, including angular velocities having zero or near-zero probabilityvalues) is divided into a set of AVRs. In either case, the angularvelocities are divided into a set of AVRs such that the maximumdimension of each AVR is not greater than twice A. This implies that theangular velocities corresponding to each AVR that is scanned by theimage sensor does not deviate from the central angular velocity of theAVR by more than the maximum relative angular velocity A.

Referring back to the plot 200, by dividing the space of reasonableangular velocities into AVRs, an AVR map may be obtained. FIGS. 3A and3B illustrate examples of AVR maps 300A and 300B respectively. The maps300A and 300B may be generated, for example, based on the plot 200,which corresponds to reasonable angular velocities for orbital debriswhen the image sensor is pointing in a particular direction (that is,orientation). The NOC 120 or the satellite 105 may generate the maps300A and 300B. Accordingly, the following sections describe the maps300A and 300B as generated by the system 100 using the plot 200.However, the maps 300A and 300B may be generated by other systems basedon other angular velocity probability distribution maps.

FIG. 3A shows an AVR map 300A in which the size of all the AVRs isuniform. The AVR map 300A includes an underlying reasonable angularvelocity probability distribution plot 302, on which AVRs, such as 304,306 and 308 are overlaid.

The reasonable angular velocity probability distribution plot 302 may bethe RAVD plot 200. The set of AVRs overlaid on the plot 302, whichinclude AVRs 304, 306 and 308, may be generated based on the maximumrelative angular velocity A, as discussed above. The AVRs computed inthe manner described above are all circular in shape, with each having aradius that is equal to A. However, it may not be possible to covercompletely a planar region, such as the plot 302, with circles of radiusA without either overlapping or missing parts of the planar region.Therefore, in some implementations, the AVRs are represented ashexagons, with distance from the center of a hexagon to each corner ofthe hexagon being limited by A. Hence, each of the AVRs in the map 300A(and also 300B), such as 304, 306 or 308, is hexagonal in shape.Representing AVRs as hexagons ensures that all areas of the plot 302 arecovered, that is, all debris orbits are captured by at least one AVR,while avoiding overlap between AVRs.

Since the size of each AVR is based on A while the underlying plot 302is pre-computed, the number of AVRs in the set of AVRs in the map 300Adepends on A. Therefore, following the dependency chain for A, thenumber of AVRs is a function of the sensor pixel size and exposure time,with the latter being dependent on the brightness of the debris. Dimdebris with a poor image sensor may have a larger number of smallerAVRs, while bright debris with an image sensor of high sensitivity mayhave a smaller number of large AVRs.

As shown in map 300A, the AVRs 304, 306 and 308 all have the same size.However, in some implementations, the size of the AVRs in a set of AVRsmay vary. FIG. 3B shows an AVR map 300B in which the size of the AVRsvary. The AVR map 300B includes an underlying angular velocityprobability distribution map 312, on which AVRs, such as 314, 316 and318, are overlaid.

An AVR is sized such that, if the image sensor is slewed at an angularspeed and in a direction that corresponds to the angular velocity of thecenter of AVR, orbital debris having angular velocities near the edge ofthe AVR can also be detected. As described previously, the size of theAVR may depend on the pixel size and the exposure time for the orbitaldebris that the image sensor is attempting to detect. The exposure time,in turn, depends on the brightness of the orbital debris being detected,the distance to the orbital debris, and the sensitivity of the imagesensor.

The apparent brightness of the orbital debris (that is, the signal levelat the image sensor generated from photons received from the orbitaldebris) follows an inverse square law. As such, orbital debris that arecloser to the image sensor require less exposure time compared toorbital debris that are farther away. Closer orbital debris also tend tomove faster (relative to the sensor) than farther orbital debris.Therefore, most orbital debris that move at very high speed may becloser to the sensor and hence, may be captured with less exposure time.This observation assumes that the orbital debris follow a set ofreasonable orbits.

Since the closer orbital debris use less integration time, the AVRs canbe bigger. That is, A is equal to (pixel dimension)/(exposure time),and, consequently, a smaller exposure time leads to a bigger A. The sizeof the AVRs, therefore, may be proportional to the magnitude of theangular velocity. Orbital debris with small angular velocities will tendto be much more distant from the image sensor and hence move moreslowly. AVRs of smaller sizes, therefore, may be necessary to detectsuch slower moving orbital debris. On the other hand, orbital debriswith larger angular velocities will tend to be moving faster and hencemay be detected by scanning using larger AVRs.

Consequently, the angular velocity probability distribution map 312 maybe divided into AVRs of varying sizes, with areas of the map thatcorrespond to smaller angular velocities being covered by smaller AVRsand areas of the map that correspond to larger angular velocities beingcovered by larger AVRs. For example, AVR 314 may be larger than AVR 316,which in turn may be larger than AVR 318. Therefore, the angularvelocities associated with AVR 314 may be greater than angularvelocities associated with AVR 316, which in turn may be greater thanthe angular velocities associated with AVR 318.

The AVR maps 300A and 300B are pre-computed before they are used fordirecting the image sensor in the search for orbital debris. An AVR mapmay be pre-computed by the GBS for multiple different image sensorpointing directions/orientations. For example, the computing devicespresent at the NOC 120 may compute the AVR maps based on computer modelsand orbital parameters of target debris and the orientation/pointingdirection of the image sensor 110 and/or satellite 105. Alternatively,in some implementations, the AVR maps 300A and 300B maps may bepre-computed by the satellite 105, for example, by executing theinstructions, which are stored in the storage device onboard thesatellite, using the one or more processors present on the satellite.The AVR maps, including, for example, AVR maps 300A and/or 300B, maythen be leveraged to generate a search schedule for the image sensor110.

FIG. 4 illustrates an exemplary process 400 that may be used fordeveloping an AVR-based search schedule for an image sensor fordetecting orbital debris. The process 400 may be used by NOC 120 togenerate the AVR maps 300A and/or 300B, develop a search schedule forthe image sensor 110 based on the AVR maps, and upload the searchschedule to the satellite 105. Alternatively, the process 400 may beused by the satellite 105 itself to generate the AVR maps 300A and/or300B and develop a search schedule for the image sensor 110.Accordingly, the following describes the process 400 as beingimplemented by the system 100. However, the process 400 also may beimplemented by other systems and system configurations.

The process 400 starts by determining the exposure time for the imagesensor based on the properties of the sensor and the properties of thedebris to be detected (402). For example, in order to determine themaximum relative angular velocity A, the properties of the sensor, suchas the noise floor, the threshold SNR and the pixel dimension, areobtained. In addition, parameters associated with the debris brightness,such as the size of the debris and the target distance, are determined.Based on the sensor and the debris properties, the exposure time of theimage sensor 110 is computed. As discussed previously, the propertiesindicated above may be obtained, for example by the NOC 120, frommanufacturer datasheets of the image sensor 110 and/or computer modelsgenerated by the computing devices at the NOC 120. Alternatively oradditionally, the properties may be obtained from data downloaded fromthe satellite 105.

The maximum relative angular velocity A is computed based on theexposure time and the image sensor pixel size (404). For example, theNOC 120 may compute A by dividing the pixel dimension in micro-radiansby the integration time in seconds.

An initial direction Do is selected for the image sensor on thespacecraft (406). For example, the NOC 120 may determine the initialdirection Do based on a location of the satellite 105 and a location ofdebris of interest.

Once D₀ is determined, a reasonable angular velocity distribution (RAVD)plot is generated for D₀ (408). For example, the NOC 120 may generatethe RAVD plot 200A based on the initial direction D₀ once D₀ isdetermined. As noted previously, the RAVD plot is specific to aparticular image sensor pointing direction and is generated based onknown debris orbit data.

Subsequently, an angular velocity region (AVR) map for D₀ is generatedbased on the RAVD plot for D₀ and the maximum angular velocity A (410).For example, the NOC 120 may generate the AVR map 300A or 300B based onthe RAVD plot 200A and the maximum relative angular velocity A. Notably,while AVR maps 300A and 300B are maps that completely cover thedistribution of reasonable angular velocities with AVRs shaped likehexagons with no overlaps or gaps, other AVR maps may include AVRs thatoverlap each other and/or that are separated by gaps. In someimplementations, the AVR map may cover only portions of the distributionof reasonable angular velocities deemed to correspond to the highestprobabilities. For example, it may be desirable to not restrict theplacement of AVRs to a hexagonal or other type of grid layout andinstead flexibly place the AVRs at whatever locations on the RAVD plotthat best cover the highest probability angular velocities, even if suchplacement results in gaps between AVRs or AVRs overlapping.

An AVR A₀ is selected from the AVR map for Do based on a debris searchstrategy (412). For example, the NOC 120 may select one of the AVRs,such as 304, 306 or 308 if the AVR map for D₀ is 300A, or 314, 316, or318 if the AVR map for D₀ is 300B. Determining which particular AVR toselect may be based on the search strategy that is implemented for theparticular search schedule being developed. In some implementations, anAVR may be selected from the AVR map using a random selection mechanism.In some other implementations, a deterministic strategy may be used toensure that new debris is detected sufficiently often. For example, theselection of an AVR may be based on the associated probabilitydistribution of the underlying RAVD map. AVRs that correspond to regionsof the RAVD map with higher probabilities of detection may be selectedmore frequently compared to AVRs that correspond to regions of the RAVDmap with lower probabilities of detection.

In some implementations, the strategy chosen may depend on the exposuretime and the expected relative speed of the orbital debris. If the imagesensor uses a very short exposure time, then it may be useful to selectAVRs and directions that are widely distributed. On the other hand, ifthe exposure time used is high, then it may be useful to scan a smallnumber of highly likely AVRs to ensure a maximum amount of detections.

Once the AVR A₀ is selected, a spacecraft search schedule is generatedthat informs the spacecraft to slew the sensor from initial direction D₀at an angular velocity corresponding to AVR A₀ (414). For example, theNOC 120 creates a search schedule for the image sensor 110. The searchschedule includes entries, with each entry based on a particular AVR.The NOC populates the first entry in the search schedule withinformation corresponding to the AVR A₀ as the initial control point,such as a time T₀ for initiating the search, the initial direction D₀and the angular velocity at the center of A₀. Therefore, the satellite105 may start the search at the time T₀ in the direction Do and scan AVRA₀ by slewing the image sensor 110 at an angular speed and in adirection corresponding to the angular velocity at the center of AVR A₀.

Once the search schedule is populated with at least one entry, it isdetermined whether the search schedule is complete (416). For example,in some implementations, the search schedule may be used to scan only asingle AVR.

If it is determined that the search schedule is not complete, a newdirection D_(i) for the image sensor at the end of rotation isdetermined (418). Notably, as the image sensor rotates while scanning anAVR, the direction of the image sensor changes. Therefore, the NOC 120may compute what the new direction for the image sensor 110 will be onceit has completed scanning AVR A₀.

In some implementations, the new direction D_(i) may be adjusted (420).For example, the search schedule may be developed such that the imagesensor is configured to capture multiple images of the same AVR byrepeating the scan of the same AVR multiple times. In such cases, once ascan ends with the image sensor pointing in a new direction, the imagesensor may be re-oriented such that the image sensor again points in thestarting direction of the AVR just scanned, and the scan of the AVR isrepeated, allowing the image sensor to capture additional images of thesame search space. This feature may be optional and may not beimplemented in all scenarios, which is indicated by the dotted linesaround (420).

Once the new direction D_(i) is determined, an RAVD plot for D_(i) isaccessed (422). As described previously, the RAVD plot 200A may bedependent on the pointing direction (i.e., orientation) of the imagesensor. Therefore, as the image sensor points in a new direction D_(i)at the end of scanning the AVR A₀, the RAVD map that is now applicablemay have changed. Consequently, the NOC 120 may compute a new RAVD mapfor the new direction D_(i). In some implementations, the NOC 120 maystore pre-computed RAVD maps for different orientations of the imagesensor 110. In such implementations, the NOC 120 may simply access, fromlocal storage, the RAVD map corresponding to the new direction D_(i).

An angular velocity region (AVR) map for D_(i) is generated based on theRAVD plot for D_(i) and the maximum angular velocity A (426). Forexample, the NOC may generate a new AVR map for the new direction D_(i),in a manner similar to that described for direction Do (410).

Once the AVR map for D_(i) is generated, an AVR A_(i) is selected fromthe AVR map for D_(i) based on the debris search strategy (428). Forexample, the NOC 120 may select an AVR A_(i) from the set of AVRscorresponding to the AVR map for D_(i), in a manner similar to thatdescribed for direction D₀ (412). In some implementations, the searchstrategy that is used for selecting A_(i) may be the same as that usedfor selecting A₀, and the same for selecting other AVRs. In some otherimplementations, different search strategies may be used for selectingdifferent AVRs.

The spacecraft search schedule is updated to inform the spacecraft toscan AVR A_(i) by slewing the image sensor from the new direction D_(i)at an angular velocity corresponding to AVR A_(i) (428). For example,the NOC 120 may populate the search schedule, which was created with AVRA₀ as the initial AVR, with a new entry corresponding to the AVR A_(i),such as a time T_(i) for starting the scan of AVR A_(i), a startingdirection D_(i) for AVR A_(i) and the angular velocity at the center ofAVR A_(i). Therefore, at the time T_(i) the satellite may slew the imagesensor 110 starting in direction D_(i) and moving at an angular speedand in a direction corresponding to the angular velocity at the centerof AVR A_(i).

After the search schedule is updated with information on the AVR A_(i),it is again determined whether the search schedule is completed (416).This check may be performed at the end of every round of updating thesearch schedule, where a round corresponds to determining the data foran entry in the search schedule for a particular selected AVR A_(i) andpopulating the search schedule with the entry to enable scanning of theselected AVR A_(i).

If there are more AVRs to scan, operations (418)-(428) are repeated. Onthe other hand, if it is determined that the search schedule iscomplete, the search schedule is communicated to the spacecraft (430).For example, the NOC 120 may send a complete search schedule to thesatellite through one of the gateways 115 a or 115 b. The completesearch schedule may include an entry corresponding to each AVR on whichthe search schedule is based.

In some implementations, each entry in the search schedule includes astart time for starting a scan, a direction of pointing the image sensor110 at the start of the scan, an angular speed and a direction in whichthe image sensor 110 is to be moved during the scan, and a stop time forterminating the scan. The angular speed and direction in which the imagesensor 110 is to be moved may correspond to the angular velocity at thecenter of the AVR associated with the entry. The stop time forterminating the scan may correspond to the time at which the imagesensor 110 reaches a direction that points to the terminating edge ofthe AVR when the image sensor 110 is slewed at the specified rate,starting from the direction and at the start time indicated by the entryin the search schedule. The next entry in the search schedule may havesimilar fields as above. The starting direction for the next entry maybe the same as the ending direction for the previous entry.

In other implementations, each entry in the search schedule includes astart time, an orientation of the image sensor 110 at the start time,and whether the sensor is on/off. In such implementations, the slewingof the image sensor may be determined from the start time and theorientation schedule. For example, two consecutive entries in the searchschedule may be: T1 O1 sensor ON; T2 O2 sensor ON. In this example, T1is start time corresponding to the first entry, O1 is the orientation ofthe image sensor at time T1 and sensor ON means that the image sensor110 will be ON at time T1. T2 is the start time corresponding to thesecond entry, O2 is the orientation of the image sensor at time T1 andsensor ON means that that the image sensor 110 will be ON at time T2.The angular speed and direction of rotation of the image sensor may bedetermined as (O2-O1) in radians divided by T2-T1. Thus, the entries inthe search schedule may imply an angular speed and a direction ofrotation of the image sensor, but may not explicitly provide the angularspeed and the direction.

FIG. 5 illustrates an exemplary process 500 that may be used forsearching for orbital debris using an image sensor on board a satellite.The process 500 may be used by the satellite 105 to slew the imagesensor 110 according to a search schedule that is developed by the NOC120, or by the satellite 105. Accordingly, the following describes theprocess 500 as being implemented by the system 100. However, the process500 also may be implemented by other systems and system configurations.

The process 500 starts with the satellite 105 receiving a searchschedule from the ground-based system (GBS) (502). For example, the NOC120 may upload the search schedule to the satellite by one of thegateways 115 a or 115 b through the satellite channel 130 a or 130 brespectively. The search schedule may have been generated by the NOC 120using the process 400.

The search schedule is read and image capture is initiated (504). Forexample, the satellite 105 may read the search schedule received fromthe NOC 120 and configure the gimbal device and the image sensor 110 tocapture images in the directions indicated by the search schedule.

In some implementations, the search schedule may include instructionsthat, when executed by the processors on board the satellite 105, directthe gimbal device to slew the image sensor 110 based on the informationprovided by the search schedule, while the image sensor 110 is operatedto capture images as it is slewed. In other implementations, the searchschedule may include only data points for the various entries.Instructions that are stored in the memory onboard the satellite andexecuted by the satellite processors may suitably interpret the datapoints for rotating the image sensor and capturing the images.

The image sensor is oriented in direction D_(i) and rotated at anangular velocity corresponding to AVR A_(i) (506). For example, uponprocessing the information in the search schedule, the onboardprocessors may operate the gimbal device to orient the image sensor 110in a direction D_(i) that is indicated as the starting directioncorresponding to the entry of the search schedule that is to beexecuted. Then, at the search start time for the entry, the onboardprocessors may trigger the gimbal device to slew the image sensor 110 atan angular speed and in a direction that is same as the angular velocityat the center of the AVR A_(i), on which the currently executed entry ofthe search schedule is based. The onboard processors may further operatethe gimbal device to stop the rotation of the image sensor 110 at a timethat corresponds to the search end time for the entry in the searchschedule.

An image is captured according to the exposure time (508). For example,while executing an entry in the search schedule, the processors onboardthe satellite 105 may operate the image sensor 110 to open its shutterand capture images in the direction it is pointing as the gimbal deviceslews the image sensor 110 as described in (506). The image sensor 110may be configured to start capturing images at the search start time forthe entry. The onboard processors may further operate the image sensor110 to stop the image capture when the exposure time of the image sensoris completed. In some implementations, the exposure time may be same asthe search end time for the entry, while in other implementations, theexposure time may end before the search end time for the entry isreached.

The images captured by the image sensor 110 may be saved to localstorage on the satellite 105. For example, the images may be saved to ahard drive or flash memory onboard the satellite.

In some implementations, additional images may be taken (510). Forexample, the search schedule may be developed such that the image sensor110 is configured to capture multiple images of the same AVR. In suchcases, the search schedule may include entries, based on which thegimbal is operated to slew the image sensor 110 back to the startingdirection of the entry that was most recently executed once the imagesensor reaches the end of the current scan. Then the gimbal again slewsthe image sensor 110 at an angular speed and in a direction that is thesame as the angular velocity used in the previous scan, while the imagesensor is operated to capture additional images of the same searchspace. This feature may be optional and may not be implemented in allsearch schedules, which is indicated by the dotted lines around (510).The additional images, if captured, may be saved to local storage on thesatellite 105, as described above.

A determination is made whether execution of the search corresponding tothe search schedule is complete (512). For example, at the end ofexecution of each entry in the search schedule, the instructions thatare executed by the satellite processors may parse the data to determinewhether there are further entries left.

If it is determined that the search corresponding to the search scheduleis not complete, then the next entry is parsed (514), and the searchprocessing is repeated based on the information corresponding to thenext entry (506)-(510).

On the other hand, if the search corresponding to the search schedule isdetermined to be complete, the images are sent to the ground-basedsystem (515). For example, the satellite 105 may send data correspondingto the images that are saved in its local storage to the NOC 120. Thedata may be downloaded to one of the gateways 115 a and/or 115 b overthe satellite channel 130 a or 130 b respectively. The receivinggateway(s) forward the data to the NOC 120 over the network 125. At theNOC, the data may be processed for detecting orbital debris in thecaptured images. In some implementations, the data may be downloadedfrom the satellite 105 periodically in batches. For example, thesatellite may collect data from several search schedules together andsend them in one transmission. In other implementations, the data may bedownloaded as they are collected. For example, the satellite 105 maysend the data for a search schedule as soon as the search is completed.

FIG. 6 illustrates an exemplary search 600 performed by an image sensoron board a satellite for detecting orbital debris. The search 600 may beperformed, for example, by the image sensor 110 based on an entry in asearch schedule developed by the NOC 120. Accordingly, the followingdescribes the search 600 as performed by components of the system 100.However, the search 600 also may be performed by other systems.

The search 600 is performed by an image sensor 602 that includes a pixel604 and has a focal point 606. The direction of the search is indicatedby arrow 608. The area of the search is given by the pyramid 610, whilethe detection frustum is 612, between the planes 612 a and 612 b.Orbital debris are indicated by 614, 616, 618, 620 and 622.

The image sensor 602 may be same as the image sensor 110. The vertex ofthe pyramid 610 is at the focal point 606 of the image sensor 602. Thearea covered by the pyramid, which is a function of the width of thepixel 604, corresponds to the AVR on which search 600 is based.

The angular speed and direction of rotation of the image sensor 602 isbased on the angular velocity at the center of the AVR on which search600 is based. The angular speed and direction of rotation of the imagesensor 602 is such that it is similar to the angular velocities oforbits within the detection frustum 612, with debris that are proximateto the plane 612 a considered to be close to the image sensor, whiledebris in the proximity of the plane 612 b considered to be at thefarthest end from the image sensor.

The orbital debris 614, 616, 618, 620 and 622 are within the detectionfrustum of the image sensor 110, with debris 622 being closest to theimage sensor, while debris 620 is the farthest away. The directions ofmovement of the debris are indicated by the arrow attached to each, withthe arrow length representing the magnitude of the angular velocity ofthe associated debris. For example, each of debris 620 and 622 isassociated with a longer arrow compared to debris 614. In addition, thearrows associated with 620 and 622 are approximately the same length.Therefore, the angular velocities of debris 620 and 622 are similar, andtheir angular velocities are greater than that of debris 614.

Based on the detection frustum, the debris 614 and 620 would be detectedby the image sensor 110. In some implementations, the image sensor maydetect the debris 614 and 620 as a single capture. The debris 622 ismoving in the same direction as the rotation of the image sensor. Sincethe tangential speed of the debris 622 is similar to that of debris 620,but the former is much closer to the image sensor compared to thelatter, the debris 622 may be moving too fast for the angular speed anddirection of rotation of the image sensor 110. Therefore, the angularvelocity of the debris 622 may not be in the AVR associated with thesearch 600, and the image sensor 110 may not be able to detect thedebris 622. In addition, the image sensor 110 may not capture images ofthe debris 616 and 618, since they are moving in the direction oppositeto the direction of movement of the image sensor 110 and consequentlythey are not in the AVR being searched.

Various implementations of the systems and techniques described here canbe realized in digital electronic circuitry, integrated circuitry,specially designed ASICs (application specific integrated circuits),computer hardware, firmware, software, and/or combinations thereof.These various implementations can include implementation in one or morecomputer programs that are executable and/or interpretable on aprogrammable system including at least one programmable processor, whichmay be special or general purpose, coupled to receive data andinstructions from, and to transmit data and instructions to, a storagesystem, at least one input device, and at least one output device.

These computer programs (also known as programs, software, softwareapplications or code) include machine instructions for a programmableprocessor, and can be implemented in a high-level procedural and/orobject-oriented programming language, and/or in assembly/machinelanguage. As used herein, the terms “machine-readable medium”“computer-readable medium” refers to any computer program product,apparatus and/or device (for example, magnetic discs, optical disks,memory, Programmable Logic Devices (PLDs)) used to provide machineinstructions and/or data to a programmable processor, including amachine-readable medium that receives machine instructions as amachine-readable signal. The term “machine-readable signal” refers toany signal used to provide machine instructions and/or data to aprogrammable processor.

Suitable processors for the execution of a program of instructionsinclude, by way of example, both general and special purposemicroprocessors, and the sole processor or one of multiple processors ofany kind of computer. Generally, a processor will receive instructionsand data from a read-only memory or a random access memory or both. Theelements of a computer may include a processor for executinginstructions and one or more memories for storing instructions and data.Generally, a computer will also include, or be operatively coupled tocommunicate with, one or more mass storage devices for storing datafiles; such devices include magnetic disks, such as internal hard disksand removable disks; magneto-optical disks; and optical disks. Storagedevices suitable for tangibly embodying computer program instructionsand data include all forms of non-volatile memory, including by way ofexample semiconductor memory devices, such as EPROM, EEPROM, and flashmemory devices; magnetic disks such as internal hard disks and removabledisks; magneto-optical disks; and CD-ROM and DVD-ROM disks. Theprocessor and the memory can be supplemented by, or incorporated in,ASICs (application-specific integrated circuits).

To provide for interaction with a user, the systems and techniquesdescribed here can be implemented on a computer having a display device(for example, a CRT (cathode ray tube) or LCD (liquid crystal display)monitor) for displaying information to the user and a keyboard and apointing device (for example, a mouse or a trackball) by which the usercan provide input to the computer. Other kinds of devices can be used toprovide for interaction with a user as well; for example, feedbackprovided to the user can be any form of sensory feedback (for example,visual feedback, auditory feedback, or tactile feedback); and input fromthe user can be received in any form, including acoustic, speech, ortactile input.

The systems and techniques described here can be implemented in acomputing system that includes a back end component (for example, as adata server), or that includes a middleware component (for example, anapplication server), or that includes a front end component (forexample, a client computer having a graphical user interface or a Webbrowser through which a user can interact with an implementation of thesystems and techniques described here), or any combination of such backend, middleware, or front end components. The components of the systemcan be interconnected by any form or medium of digital datacommunication (for example, a communication network). Examples ofcommunication networks include a local area network (“LAN”), a wide areanetwork (“WAN”), and the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made.

In addition, the logic flows depicted in the figures do not require theparticular order shown, or sequential order, to achieve desirableresults. In addition, other steps may be provided, or steps may beeliminated, from the described flows, and other components may be addedto, or removed from, the described systems. Accordingly, otherembodiments are within the scope of the following claims.

What is claimed is:
 1. A method performed by a network device, themethod comprising: determining an exposure time associated with an imagesensor that is coupled to a spacecraft and configured to capture animage of a target object orbiting the Earth; computing a first relativeangular velocity associated with the target object based on the exposuretime and a physical dimension of the image sensor; identifying a firstpointing direction of the image sensor for initiating a search for thetarget object; accessing known orbital data for the target object;generating, based on the first pointing direction and the known orbitaldata, a first set of angular velocity regions (AVRs) that indicateprobabilities of the target object having different angular velocitiesas viewed by the image sensor when the image sensor is pointing in thefirst pointing direction, wherein each AVR has a central angularvelocity and size of an AVR is limited by the first relative angularvelocity; selecting a first AVR from the first set of AVRs for scanningby the image sensor; and generating a search schedule that includes afirst entry to instruct the spacecraft to search for the target objectin the first AVR by rotating the image sensor, starting at the firstpointing direction, at an angular speed and in a direction correspondingto the central angular velocity of the first AVR, wherein the networkdevice includes a satellite ground station, and wherein the spacecraftincludes a satellite.
 2. The method of claim 1, wherein the physicaldimension of the image sensor includes a size of a pixel of the imagesensor, and wherein computing the first relative angular velocitycomprises dividing the size of the pixel by the exposure time.
 3. Themethod of claim 1, further comprising: determining whether the searchschedule is complete; based on determining that the search schedule isnot complete, determining a second pointing direction of the imagesensor at completion of scanning the first AVR; generating, based on thesecond pointing direction and the orbital data, a second a second set ofAVRs that indicate probabilities of the target object having differentangular velocities as viewed by the image sensor when the image sensoris pointing in the second pointing direction; selecting a second AVRfrom the second set of AVRs for scanning by the image sensor; and addinga second entry to the search schedule that instructs the spacecraft tosearch for the target object in the second AVR by rotating the imagesensor, starting at the second pointing direction, at an angular speedand in a direction corresponding to the central angular velocity of thesecond AVR.
 4. The method of claim 3, wherein a number of AVRs in thesecond set is different from a number of AVRs in the first set.
 5. Themethod of claim 1, further comprising: determining whether the searchschedule is complete; and based on determining that the search scheduleis complete, transmitting the search schedule to the spacecraft.
 6. Themethod of claim 5, further comprising: receiving, at the spacecraft andfrom the network device, the search schedule; reading, by thespacecraft, the first entry in the search schedule; based on reading thefirst entry, slewing, by the spacecraft, the image sensor starting fromthe first pointing direction for scanning the first AVR; andcontrolling, by the spacecraft, the image sensor for recording sensorreadings as the image sensor scans the first AVR.
 7. The method of claim6, further comprising: determining, by the spacecraft, whether there areadditional entries in the search schedule; based on determining thatthere are additional entries in the search schedule, reading, by thespacecraft, a second entry in the search schedule that includesinstructions to search for the target object in a second AVR by rotatingthe image sensor, starting at a second pointing direction, at an angularspeed and in a direction corresponding to the central angular velocityof the second AVR; responsive to reading the second entry, slewing, bythe spacecraft, the image sensor starting from the second pointingdirection for scanning the second AVR; and controlling, by thespacecraft, the image sensor for recording sensor readings as the imagesensor scans the second AVR.
 8. The method of claim 1, wherein thetarget object includes orbital debris.
 9. The method of claim 1, whereinthe exposure time includes a time used by the image sensor for recordingsensor readings, the exposure time based on one or more of a noisefloor, a threshold signal-to-noise ratio (threshold SNR) associated withthe image sensor, a size of the target object, or a distance of thetarget object from the spacecraft.
 10. The method of claim 1, whereinthe size of an AVR is proportional to a magnitude of the angularvelocity at the center of the AVR, the size of an AVR being smaller fora smaller angular velocity at the center of the AVR in comparison to alarger angular velocity at the center of the AVR.
 11. The method ofclaim 1, wherein selecting the first AVR from the first set of AVRscomprises selecting the first AVR based on one of a random selectionstrategy or a probability of detection of the target object that isassociated with each AVR in the first set of AVRs.
 12. A deviceincluding a storage medium storing instructions that, when executed byone or more processors, are configured to cause the one or moreprocessors to perform operations comprising: determining an exposuretime associated with an image sensor that is coupled to a spacecraft andconfigured to capture an image of a target object orbiting the Earth;computing a first relative angular velocity associated with the targetobject based on the exposure time and a physical dimension of the imagesensor; identifying a first pointing direction of the image sensor forinitiating a search for the target object; accessing known orbital datafor the target object; generating, based on the first pointing directionand the known orbital data, a first set of angular velocity regions(AVRs) that indicate probabilities of the target object having differentangular velocities as viewed by the image sensor when the image sensoris pointing in the first pointing direction, wherein each AVR has acentral angular velocity and size of an AVR is limited by the firstrelative angular velocity; selecting a first AVR from the first set ofAVRs for scanning by the image sensor; and generating a search schedulethat includes a first entry to instruct the spacecraft to search for thetarget object in the first AVR by rotating the image sensor, starting atthe first pointing direction, at an angular speed and in a directioncorresponding to the central angular velocity of the first AVR, whereinthe device includes a satellite ground station, and wherein thespacecraft includes a satellite.
 13. The device of claim 12, wherein thephysical dimension of the image sensor includes a size of a pixel of theimage sensor, and wherein computing the first relative angular velocitycomprises dividing the size of the pixel by the exposure time.
 14. Thedevice of claim 12, wherein the instructions are configured to cause theone or more processors to perform operations comprising furthercomprising: determining whether the search schedule is complete; basedon determining that the search schedule is not complete, determining asecond pointing direction of the image sensor at completion of scanningthe first AVR; generating, based on the second pointing direction andthe orbital data, a second a second set of AVRs that indicateprobabilities of the target object having different angular velocitiesas viewed by the image sensor when the image sensor is pointing in thesecond pointing direction; selecting a second AVR from the second set ofAVRs for scanning by the image sensor; and adding a second entry to thesearch schedule that instructs the spacecraft to search for the targetobject in the second AVR by rotating the image sensor, starting at thesecond pointing direction, at an angular speed and in a directioncorresponding to the central angular velocity of the second AVR.
 15. Thedevice of claim 14, wherein a number of AVRs in the second set isdifferent from a number of AVRs in the first set.
 16. The device ofclaim 12, wherein the instructions are configured to cause the one ormore processors to perform operations comprising further comprising:determining whether the search schedule is complete; and based ondetermining that the search schedule is complete, transmitting thesearch schedule to the spacecraft.
 17. The device of claim 16, whereinthe instructions are configured to cause the one or more processors toperform operations comprising further comprising: receiving, at thespacecraft and from the device, the search schedule; reading, by thespacecraft, the first entry in the search schedule; based on reading thefirst entry, slewing, by the spacecraft, the image sensor starting fromthe first pointing direction for scanning the first AVR; andcontrolling, by the spacecraft, the image sensor for recording sensorreadings as the image sensor scans the first AVR.
 18. The device ofclaim 17, wherein the instructions are configured to cause the one ormore processors to perform operations comprising further comprising:determining, by the spacecraft, whether there are additional entries inthe search schedule; based on determining that there are additionalentries in the search schedule, reading, by the spacecraft, a secondentry in the search schedule that includes instructions to search forthe target object in a second AVR by rotating the image sensor, startingat a second pointing direction, at an angular speed and in a directioncorresponding to the central angular velocity of the second AVR;responsive to reading the second entry, slewing, by the spacecraft, theimage sensor starting from the second pointing direction for scanningthe second AVR; and controlling, by the spacecraft, the image sensor forrecording sensor readings as the image sensor scans the second AVR. 19.The device of claim 12, wherein the target object includes orbitaldebris.
 20. The device of claim 12, wherein the exposure time includes atime used by the image sensor for recording sensor readings, theexposure time based on one or more of a noise floor, a thresholdsignal-to-noise ratio (threshold SNR) associated with the image sensor,a size of the target object, or a distance of the target object from thespacecraft.
 21. The device of claim 12, wherein the size of an AVR isproportional to a magnitude of the angular velocity at the center of theAVR, the size of an AVR being smaller for a smaller angular velocity atthe center of the AVR in comparison to a larger angular velocity at thecenter of the AVR.
 22. The device of claim 12, wherein selecting thefirst AVR from the first set of AVRs comprises selecting the first AVRbased on one of a random selection strategy or a probability ofdetection of the target object that is associated with each AVR in thefirst set of AVRs.